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No, the port 113 doesn't appear in the list, and I even tried rebooting mIRC.

Did you turn off "enable only when connecting" in the Identd dialog? If you run a program like TcpView does it show that mIRC is listening on identd port 113?

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Note that I tried to /socklisten -p test 8002 right after, and it correctly appeared in the list.

That is very odd - /socklisten uses the same method as identd.

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Yes the external IP displayed is correct.

When you say it is correct, do you mean the "External IP" displayed in the left hand column for an entry in PortForward? Ideally, you will need to confirm this for the port 113 that mIRC creates, however since you are not seeing port 113 in PortForward, something else seems to be going on.